Abstract
We study by direct numerical simulation the motion of incompressible fluid contained
in an ellipsoid of revolution with ellipticity 0.1 or less which rotates about its axis
of symmetry and whose rotation axis is executing precessional motion. A solution
to this problem for an inviscid fluid given by Poincaré (1910) predicts motion of
uniform vorticity. The simulations show how the orientation of the average vorticity
of a real fluid is influenced by both pressure and viscous torques exerted by the
boundaries. Axisymmetric shear layers appear which agree well with those observed
experimentally by Malkus (1968). Shear caused by deviations from a velocity field
with uniform vorticity triggers an instability consisting of waves propagating around
the average rotation axis of the fluid. The Ekman layers at the boundaries may also
become unstable.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
93 articles.
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